He is expected to be replaced in the Welsh set-up by predecessor Kit Symons.
Having been Wales manager Chris Coleman’s number two since 2012, Symons left in June 2015 to take charge of Fulham, but the 45-year-old was sacked six month later.
That paves the way for Symons to return to his international role with Coleman, his former Wales and Fulham centre-back partner.
Trollope was with Wales during their historic Euro 2016 campaign, helping his country reach a major tournament semi-final for the first time.
He had been juggling international duties with his club commitments, having joined Slade’s coaching team at Cardiff in February 2015.
Slade was removed as manager of the Championship club at the end of last season and was initially given a new role as head of football, but lasted only 28 days in the job before leaving the club.
That allowed former Wales, Derby and Fulham midfielder Trollope to take the reins.
He will be assisted by ex-Cardiff boss Lennie Lawrence – who he worked with at Bristol Rovers – and James Rowberry, while Wales’ head of performance Ryland Morgans has joined the Bluebirds as performance director.